Abstract
Let R be a Noetherian domain with quotient field K. Let A be an integral domain which contains R and whose elements are algebraic over K. We define \({{\rm Eass}_{R}(A/R)}\) to be the set of prime ideals \({\mathfrak{p}}\) ’s of R such that \({\mathfrak{p}}\) is a prime divisor of a generalized denominator ideal I[β] for some \({\beta \in A}\). Assume that \({A = R[\alpha_{1}, \ldots,\alpha_{n}]}\). We investigate the relation between \({{\rm Eass}_{R}(A/R)}\) and \({\cup_{i = 1}^{n} {\rm Ass}_{R}(R/I_{[\alpha_{i}]})}\). Furthermore, for a finite subset Δ of \({{\rm Eass}_{R}(A/R)}\), we construct the subring A Δ of A such that A Δ is the largest among those B’s with .
![](http://media.springernature.com/full/springer-static/image/art%3A10.1007%2Fs40065-013-0082-1/MediaObjects/40065_2013_82_Article_Figa_HTML.gif)
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Baba K., Yoshida K.: Extensions of a Noetherian domain R. Arab. J. Sci. Eng. 26(1C), 45–49 (2001)
Baba K., Yoshida K.: Anti-integral extensions R[α]/R and invertibility of αn − a. Tamkang J. Math. 35(1), 1–12 (2004)
Bourbaki N.: Algèbre Commutative. Hermann, Paris (1965)
Kaplansky I.: Commutative Rings. The University of Chicago Press, Chicago (1974)
Matsumura H.: Commutative Algebra, 2nd edn. Benjamin, New York (1980)
Oda S., Sato J., Yoshida K.: High degree anti-integral extensions of Noetherian domains. Osaka J. Math. 30(1), 119–135 (1993)
Yoshida K.: On birational-integral extension of rings and prime ideals of depth one. Jpn. J. Math. 8(1), 49–70 (1982)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
This article is published under license to BioMed Central Ltd.Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
About this article
Cite this article
Baba, K., Yoshida, Ki. The set of prime divisors of generalized denominator ideals. Arab. J. Math. 2, 333–343 (2013). https://doi.org/10.1007/s40065-013-0082-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40065-013-0082-1